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The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. Using ingredients of the group averaging method to solve constraints one can nevertheless introduce a classical coordinate time into the quantum theory, and use it to investigate the way a semiclassical continuous description emerges from discrete quantum evolution. Applying this technique to test effective classical equations of loop cosmology and their implications for inflation and bounces, we show that the effective semiclassical theory is in good agreement with the quantum description even at short scales.

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Physical Review D - Particles, Fields, Gravitation and Cosmology